https://file.aiquickdraw.com/mathbot/file/1725870732634dtnxj0th.jpg

Let's go through the questions one by one and work on solutions.

### 3. (a) A projectile is fired at an angle, \(\theta\), to the horizontal with velocity, \(u\). Show that at any time, \(t\), during the motion:
#### (i) The horizontal component of the velocity is independent of \(t\).
The horizontal velocity component is given by:
\[
v_x = u \cos \theta
\]
Since there are no horizontal forces acting (neglecting air resistance), the horizontal velocity remains constant throughout the motion. Hence, it is independent of time \(t\).

#### (ii) The vertical component of the velocity depends on \(t\).
The vertical velocity component is given by:
\[
v_y = u \sin \theta - g t
\]
Where:
- \(u \sin \theta\) is the initial vertical velocity,
- \(g\) is the acceleration due to gravity, and
- \(t\) is time.

This shows that the vertical velocity decreases with time, due to the effect of gravity, so it depends on \(t\).

### (b) State the assumption on which projectile motion is based.
Projectile motion is based on the assumption that:
- The only force acting on the projectile after it is fired is gravity.
- Air resistance is neglected, meaning no horizontal forces act on the projectile.

---

### 4. State three differences between geostationary satellites and polar satellites.

1. **Orbit:**
   - Geostationary satellites orbit above the equator in a fixed position relative to Earth, while polar satellites move over Earth's poles in a north-south orbit.
   
2. **Altitude:**
   - Geostationary satellites are at a higher altitude (around 35,786 km), while polar satellites orbit at lower altitudes (about 200 to 1,200 km).

3. **Coverage:**
   - Geostationary satellites cover a specific region, making them ideal for communication, whereas polar satellites cover the entire Earth as the planet rotates, making them useful for global monitoring.

---

### 5. (a) Using the kinetic theory, explain the term "diffusion of fluid molecules."

According to kinetic theory, diffusion is the process by which fluid molecules move from a region of higher concentration to a region of lower concentration. This happens because molecules in a fluid are in constant random motion, and over time, this random motion causes molecules to spread out evenly in the available space.

---

Would you like more details or further clarification on any of these solutions?

### Related Questions:
1. What factors influence the range of a projectile?
2. How does air resistance affect projectile motion?
3. What are the applications of geostationary satellites in daily life?
4. Why are polar satellites preferred for weather monitoring?
5. How does temperature affect the rate of diffusion of fluid molecules?

### Tip:
For projectile motion, always break the initial velocity into horizontal and vertical components using trigonometric functions!

A projectile is fired at an angle, θ, to the horizontal with velocity, u. Show that at any time, t, during the motion: (i) the horizontal component of the velocity is independent of t; (ii) the vertical component of the velocity depends on t.

Explore the concepts of projectile motion with an emphasis on the independence of horizontal velocity and the time-dependence of vertical velocity. Learn how trigonometry and the basic principles of kinematics apply to real-world problems.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation